According to the FAA, if you're using an airport with LPV only (no ILS or other ground-based navaid approach) as your alternate airport, you need weather minimums that meet the LNAV or circling MDA, or the LNAV/VNAV DA if you're equipped to fly it.
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You need to name an alternate airport on your IFR flight plan if, for the period of time one hour before and one hour after your estimated time of arrival, the weather is forecast to include a ceiling of 2,000 feet agl and/or visibilities less than three statute miles (the 1-2-3 rule).